the discriminant is the bit under the squaer root sign in the quadratic formula
when you have
ax^2+bx+c=0
the discriminant is \(b^{2}-4ac\)
if
discriminant>0 then have 2 real solutions/roots
discriminant=0 then have 1 real solution/root
discriminat<0 then have no real roots (2 imaginary roots)
-3x^2+x-1=0
a=-3
b=1
c=-1
\(1^{2}-4(-3)(-1)\)=1-12=-11
-11<0
has zero real solutions
